Nicolas Gisin is an experimental physicist who has extended the tests of quantum entanglement and nonlocality (the EPR experiment) to many kilometers from his lab in Geneva. His work has confirmed the correctness of quantum mechanics, and with it the irreducible indeterminacy involved in quantum mechanical measurements.

Despite his critical work that grounds quantum physics, Gisin has been active in searching for alternative mathematical formulations of quantum theory, especially ones that might replace the ad hoc assumption of wave functions "collapsing" when measurements are made.

Alternatives proposed by GianCarlo Ghirardi and his colleagues replace the linear Schrödinger equation for the time evolution of the wave function with a nonlinear equation that includes explicit stochastic terms.

Gisin also has explored the paradoxical interpretations of his nonlocality experiments. The perfect nonlocal correlation of distant spin states suggests that information is traveling between the two widely separated measurements of electrons in an entangled spin state at velocities greater than the speed of light.

This is of course impossible, but Gisin speculates that some "influence" may be affecting both experiments coming from "outside space and time." Gisin says he means by this that "there is no story in space and time" to account for nonlocality. This is of course because the collapse of probabilities is instantaneous (not therefore "in time?") and happens everywhere (surely "in all space?").

If there were such influences, they might provide an explanation for deterministic theories, "some sort of hyper-determinism that would make all Science an illusion," says Gisin. He explains:

We have seen that any proper violation of a Bell inequality implies that all possible future theories have to predict nonlocal correlations. In this sense it is Nature that is nonlocal. But how can that be? How does Nature perform the trick? Leaving aside some technical loopholes, like a combination of detection and locality loopholes, the obvious answer, already suggested by John Bell, is that there is some hidden communication going on behind the scene. A first meaning of "behind the scene" could be "beyond today's physics", in particular beyond the speed limit set by relativity. We have seen how this interesting idea can be experimentally tested and how difficult it is to combine this idea with no-signaling. Hence, it is time to take seriously the idea that Nature is able to produce nonlocal correlations. There are several ways of formulating this:

Determinsim is a physical hypothesis that denies free will, and it is false

I know that I enjoy free will much more than I know anything about physics. Hence, physics will never be able to convince me that free will is an illusion. Quite the contrary, any physical hypothesis incompatible with free will is falsified by the most profound experience I have about free will.

So, would I have rejected Newtonian classical mechanics had I lived before quantum physics? Probably not. Indeed, classical physics leaves open the possibility that free will can somehow interface with the deterministic Newtonian equations: free will could set-up some potential that could slightly influence particles's motion. This would be something like Descartes pineal gland. In standard quantum physics such an interface between free will and physics could be even simpler: free will could influence the probabilities of quantum events. This is, admittedly, a vague and not very original idea; but important is that there is no obvious definite contradiction between free will and standard quantum physics.

The experimental setup for quantum entanglement tests is theoretically simple but experimentally difficult. Two spin 1/2 electrons are prepared in a state, say with opposing spins so the total spin angular momentum of the electrons is zero. They are said to be in a singlet state. Most recent studies, like Gisin's, used entangled polarized photon pairs.)

Two experimenters (call them A and B) measure the electron spins at some later time.

The conservation of angular momentum requires that should one of these electrons be measured with spin up, the other must be spin down. This is what is described as "nonlocal" correlation of the spin measurement results.

A simpler way of looking at the problem is to consider the conservation of angular momentum, a law of nature that can not be violated. What would the lack of "correlation" between electron spins look like? It would include some spin-up measurements by experimenter A at the same time as spin-up measurements by experimenter B.

But this is a clear violation of the conservation law for angular momentum.

This conservation law in no way depends on supra-luminal communications between particles. Consider two electrons at opposite ends of the Andromeda galaxy, say 100,000 light years apart. As they revolve around the center of the galaxy, they conserve their orbital angular momenta perfectly.

We might say, with Gisin, that conservation laws are "outside space-time."

A few years later, he again questioned whether continuous theories, with their infinities and singularities, would be the final answer to what is real.

In the Schrodinger equation, absolute
time, and also the potential energy, play a decisive role, while
these two concepts have been recognized by the theory of
relativity as inadmissible in principle. If one wishes to escape
from this difficulty, he must found the theory upon field and
field laws instead of upon forces of interaction. This leads us
to apply the statistical methods of quantum mechanics to fields,
that is, to systems of infinitely many degrees of freedom. Although
the attempts so far made are restricted to linear equations,
which, as we know from the results of the general theory
of relativity, are insufficient, the complications met up to now
by the very ingenious attempts are already terrifying...

To be sure, it has been pointed out that the introduction
of a space-time continuum may be considered as contrary to
nature in view of the molecular structure of everything which
happens on a small scale. It is maintained that perhaps the success
of the Heisenberg method points to a purely algebraical
method of description of nature, that is, to the elimination of
continuous functions from physics. Then, however, we must
also give up, on principle, the space-time continuum...

In view of this situation, it seems to be entirely justifiable
seriously to consider the question as to whether the basis of
field physics cannot by any means be put into harmony with
quantum phenomena. Is this not the only basis which, with
the presently available mathematical tools, can be adapted to
the requirements of the general theory of relativity? The belief,
prevailing among the physicists of today, that such an attempt
would be hopeless, may have its root in the unwarranted assumption
that such a theory must lead, in first approximation,
to the equations of classical mechanics for the motion of corpuscles,
or at least to total differential equations. As a matter
of fact, up to now we have never succeeded in a field-theoretical
description of corpuscles free of singularities, and we can, a
priori, say nothing about the behavior of such entities. One
thing, however, is certain: if a field theory results in a representation
of corpuscles free of singularities, then the behavior
of these corpuscles in time is determined solely by the differential
equations of the field.

"I tend more and more to the opinion that one cannot come
further with a continuum theory."

Einstein in his later years grew even more pessimistic about the possibilities for deterministic continuous field theories, by comparison with indeterministic and statistical discontinuous particle theories like those of quantum mechanics.

He wrote his friend Michele Besso in 1954 to express his lost hopes for a continuous field theory like that of electromagnetism or gravitation,

"I consider it quite possible that physics cannot be based on the field concept, i.e:,
on continuous structures. In that case, nothing remains of my entire castle in the
air, gravitation theory included, [and of] the rest of modern physics."

quoted in Subtle is the Lord..., Abraham Pais, 1982, p.467

The fifth edition of The Meaning of Relativity included a new appendix on Einstein's field theory of gravitation. In the final paragraphs of this work, his last, published posthumously in 1956, Einstein wrote:

Is it conceivable that a field theory permits one to
understand the atomistic and quantum structure of reality ?
Almost everybody will answer this question with "no"...

One can give good reasons why reality cannot at all
be represented by a continuous field. From the quantum
phenomena it appears to follow with certainty that a finite
system of finite energy can be completely described by a
finite set of numbers (quantum numbers). This does not
seem to be in accordance with a continuum theory, and
must lead to an attempt to find a purely algebraic theory
for the description of reality. But nobody knows how to
obtain the basis of such a theory.

The Meaning of Relativity, 1956, pp.165-66

Finally, we should note that Einstein was greatly impressed by the work of two great mathematicians, Leopold Kronecker and Richard Dedekind.

Kronecker famously argued that the continuum is a human creation. He said, "God made the integers, all else is the work of man." ( "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk"). Kronecker gained a measure of control over the infinities and singularities of continua with his "Kronecker delta," which is infinitely tall but infinitesimally wide, like Paul Dirac's later delta function, it integrates to unity.

A few years later, Dedekind echoed Kronecker, saying "the negative and fractional numbers have been created by the human mind." (Essays on the Theory of Numbers, p.4) Dedekind was the source for one of Einstein's most famous phrases, the "free creation of the human mind"

"Physical concepts are free creations of the human mind, and are not, however they may seem, uniquely determined by the external world."

From Information Philosophy

All the fields of physics, gravitation, electromagnetism, nuclear, and even the quantum wave function, are descriptions that enable accurate predictions of the properties of a test particle at a pint in the field. As such, fields are abstract, immaterial, information about concrete, material, objects.

In the case of quantum mechanics, the wave function provides only statistical information about individual particles. Quantum theory is thus a statistical, and therefore incomplete theory, as Einstein knew well, though his colleagues all dismissed his thinking.